Well, as in the demo you are limited both in time and in the amount of magic you can get your hands on...
High scales, especially those that give results immediately. Growth/Death is slow. Temperature is best left at the national preference (remember that it might not be 0!). Luck... depends. Production is probably nice as you will get more units and small income boost.
Take a strong, cheap pretender, like Wyrm. Take Order +3, Production +3, temperature depending on race, growth +1 if you need supplies (Jotunheim), else 0. Either best castle that is fast to build or one that provides most bonuses, that is Wizard's Tower/ Fortified City. If your race does not need many resources, consider 80 pt Castle and building more of them.
Consider Drain and Growth. Drain will slower your research, but demo will limit that any way. Growth lowers supplies, but other effects are (small reduction in population, small amount of tax loss) almost painless in 40 turns. If you have points (Ulm taking high drain, Jotun/Abysia/Machaka taking temperature scale(s)) give your Wyrm one point in Fire or two points in Water. Fire gives you Fire Shield (Enchantment 1), water Quickness (alteration 2) and Breath of Winter( enchantment 1).
Start game with small-ish map, few computer nation(s), and independents at 5. This will hopefully slow computers down more than you.
Wait for a turn, recrtuiting priest (holy 3 or 4) or mage and units of your choice. Hard to say more without knowing your race. Generally, go for high hitpoints and armor, but look at numbers too. 10 warriors with 10 hits and 13 prot. are better than 2 with 11/18. Research Enchantment if your Wyrm had magics, else you can not as you have no mages.
Host turn.
Look if there are any shortbows, druids/woodmen, militia/light infantry etc. "easy" provinces. Do NOT attack any provinces which have knights and/or longbowmen (always together but you might not see both), bloodhenge druid/dark vines, barbarian or other "hard" provinces.
Choose an easy province. Take your Wyrm. Conquer it. At the same time, consider if your "real" army is ready to try the same. You might lose your Wyrm and/or too many soldiers, but both should be strong enough if you choose your fights carefully.
When you start to have gold flowing in, build second fortress at a suitable province. Remember that the resources of that province are effectively doubled and that the fortress takes its admin-value % of resources from neighbouring provinces.
If you have (preferably cheap) nature mages and atleast 1 gem income:
Research Conjuration 1 for Vine men. Press 'M' and choose Vine Men as monthly ritual. If/when you get to Construction 2, forge Vine Crown and give it to your summoner. You get more vine men this way. If you have mage(s), search for nature sites at forests. Nature sites are most commonly found there.
With death mages, research Enchantment 1 and cast Reanimation. Be careful about priests. If you are Jotunheim, remember that you can get undead GIANTS!
C'tis gets undead lizards. Search for sites at provinces that have more Death scale than normal, but remember that computer might have taken some even if you didn't.
Else, research Evocation for elemental/astral attack spells or Construction for items. Nice items to give to your Wyrm at Construction 2:
1S: Pendant of Luck (50% of hits/arrows/spells negated), 1E: Black Steel helmet, 1D: Horror Helmet, 1N: Horned Helmet, 2A: Amulet of Missile Protection, 1E:Bracers of Protection, 2N: Cat charm.
Constr. 4:
E1: Girdle of Might, S1: Amulet of Antimagic, 3A: Flying Carpet, 2A: Dancing Trident, 2N: Ring of Regeneration/ Amulet of Resilience/ Lycanthropos' Amulet. The Last one only if you have no magics, berserk prevents spellcasting and the L's amulet automagically makes him berserk.
If you are Arcoschepale and your Wyrm gets a nasty battle affliction, use your Priestess to heal it. With other nations, no luck. If you have no magics killing him and calling back might heal some of them, though. If you have, death taxes magics so it is not a good idea.
At some point, either the computer will trash you, you hit the time limit or you will win. You might be the (almost) sure winner when you hit the limit even if you weren't able to finish your opponents. Count them as wins.
Help, read all the faqs, playing demo, dont know how to PLAY...
Hybrid Mode
